90.4.18 problem 19

Internal problem ID [25113]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 59
Problem number : 19
Date solved : Thursday, October 02, 2025 at 11:50:32 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\tan \left (t \right ) y+\sec \left (t \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 10

ode:=diff(y(t),t) = tan(t)*y(t)+sec(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (t +c_1 \right ) \sec \left (t \right ) \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 12

ode=D[y[t],{t,1}] == y[t]*Tan[t]+Sec[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to (t+c_1) \sec (t) \end{align*}

✓ Sympy. Time used: 0.357 (sec). Leaf size: 8

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-y(t)*tan(t) - sec(t) + Derivative(y(t), t),0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = \frac {C_{1} + t}{\cos {\left (t \right )}} \]